NASIRIYA, Iraq (CNN) --U.S. Army soldier Jessica Lynch, a prisoner of war whose unit was ambushed near Nasiriya on March 23, was rescued from an Iraqi hospital early Wednesday, U.S. military officials announced.

Lynch, 19, a private first class who had been listed as missing, suffered multiple serious gunshot wounds in the ambush that led to her capture and went through "quite an ordeal," Pentagon sources said. She is in stable condition.

The sources said the rescue mission had been planned for several days and involved a joint special operations team backed by U.S. Marines.

They also were searching for Ali Hassan al Majeed, a cousin of Saddam Hussein known as "Chemical Ali," accused of masterminding gas attacks on Kurdish villages in 1988, one source said.

"There were other people [Iraqis] there we were interested in getting," a military source said, some of whom may have been captured.

Marines staged an offensive in Nasiriya as a diversion while Lynch was rescued from a hospital by a special operations unit, CNN Correspondent Jason Bellini reported from the scene. The hospital was described as a Fedayeen Saddam paramilitary stronghold.

U.S. forces knocked out the city's lights just before midnight. Shortly afterward, several explosions were heard near the hospital, said CNN Correspondent Alessio Vinci, who is with the 1st Marine Expeditionary Force and witnessed part of the operation.

Marine tanks and armored vehicles approached the hospital under the cover of darkness, he said.

The Americans encountered moderate resistance from inside the hospital and a nearby building, and Lynch was taken from the hospital in the first few minutes of the operation, Vinci said.

The paramilitary squad members sometimes dress in civilian clothing to hide in the city of Nasiriya, only to "come out of the woodwork" sporadically to attack the American troops, Bellini reported.

Bellini is accompanying the artillery component of the 15th Marine Expeditionary Unit, which is part of the 1st MEF.

The orders for the rescue mission came from the head of the U.S. Central Command, one official said. The rescuers arrived by helicopter in early evening, secured the building by gunfire and forced their way inside.

"General [Tommy] Franks ordered this operation, and it was a success," said Jim Wilkinson, a Central Command spokesman.

"She's safe in coalition hands, and I'm sure she's happier than she was," he said. "America does not leave heroes behind, and there are other heroes we want to go get."

Wearing a big yellow ribbon on his blue plaid shirt, Lynch's father, Greg Lynch Sr., had trouble describing the emotions he had when he heard his daughter was safe in a hospital and in good health.

"I can't express what it was -- couldn't talk," he told CNN affiliate WCHS-TV, from his home in Palestine, West Virginia. "We're just glad it happened. ... We believed, still believed, that she was hiding out and that she wasn't a capture."

"I didn't realize that it was going to be this soon," said Lynch's brother, Greg Jr. "It's extremely good news."

A relative told CNN from Lynch's hometown of she was taken to a hospital in coalition controlled territory.

Lynch has already spoken with her parents, said Jean Offutt, a public affairs officer at Fort Bliss, Texas, where Lynch's unit, the Army's 507th Maintenance Company, was based.

"They're very happy to hear from her -- jubilant, joyful," Offutt said.

Bush: 'That's great'

President Bush was told at about 5 p.m. Tuesday that Lynch had been rescued and said, "That's great." An administration official declined to say whether Bush was told of the operation in advance.

Lynch, a supply clerk with the 507th, was listed as missing after an ambush by Iraqi forces near Nasiriya March 23 when unit members took a wrong turn after fighting near the city. (What happened to the 507th?)

Two U.S. soldiers were known to have been killed in the ambush and five others were taken prisoners of war by Iraqi forces and later shown being questioned on Iraqi TV. Lynch was listed as one of the eight missing. That tally now stands at seven.

The official overall number of American POWs also stands at seven, including two Army Apache helicopter pilots captured after their craft went down in enemy territory.

Offutt said Lynch's rescue gave hope to the families of the other 507th members who were involved in the ambush.

"I think they've been encouraged by this," Offutt said. "I know they're not giving up hope and that they'll keep hoping that their loved ones will be coming back as well."

EDITOR'S NOTE:This report was written in accordance with Pentagon ground rules allowing so-called embedded reporting in which journalists join deployed troops. Among the rules accepted by all participating news organizations is an agreement not to disclose sensitive operational details.